You have this solution to Maxwell's equations in vacuum:
$$\widetilde{\mathbf{E}}(x,y,z,t) = \widetilde{\mathbf{E}}_0 \exp\left[i\left(\mathbf{k}\cdot\mathbf{r} - \omega t\right)\right]$$
If this wave travels in the $y$ direction, is polarized in the $x$ direction, and has a complex phase of 0, what is the $x$ component of the physical wave?
1. $E_x = E_0 \ cos\left(kx-\omega t\right)$
2. $E_x = E_0 \ cos\left(ky-\omega t\right)$
3. $E_x = E_0 \ cos\left(kz-\omega t\right)$
4. $E_x = E_0 \ cos\left(k_x x+k_y y-\omega t\right)$
5. Something else
Note:
* Correct Answer: B
The electric fields of two EM waves in vacuum are both described by:
$$\mathbf{E} = E_0 \sin(kx-\omega t)\hat{y}$$
The "wave number" $k$ of wave 1 is larger than that of wave 2, $k_1 > k_2$. Which wave has the larger frequency $f$?
1. Wave 1
2. Wave 2
3. impossible to tell
Note:
* Correct Answer: A
* Same speed and thus wavelength of 1 is smaller, so frequency is higher